MONTREAL -- In his four previous shutouts this season, Carey Price has always focused more on the victory than the zero on the scoreboard.

But Price's fifth shutout Saturday afternoon was a case where that zero on the scoreboard was an essential part of the 2-0 Montreal Canadiens victory over the New York Rangers.

"These (shutouts) are secondary, but today it felt like it was necessary," Price said after stopping 35 shots, including 19 in the third period as the Rangers went all out to try and tie a 1-0 game. "Our guys played really well defensively. We knew it could be a 1-0 or 2-0 game."

Scott Gomez provided all the offense Price would require late in the second period for Montreal and Tomas Plekanec scored his 18th of the season into an empty net to seal the victory at 19:22 of the third.

With the victory, the sixth-place Canadiens (30-18-5) widened the gap over the seventh-place Rangers (29-22-4) to three points in the Eastern Conference standings.

"When you look at the (standings) board, if you think you're comfortable … these are must-wins," said Gomez, who snapped a 10-game goalless drought with his second game-winner of the season. "We want to get in a position where we're gearing towards the playoffs, not trying to get in."

The Canadiens also beat their Original Six rivals from New York for a fifth straight time dating back to last January, allowing the Rangers only four goals over that span.

Price was able to outduel Rangers backup Martin Biron in a true goaltending battle. Biron was the busier goalie through two periods with 22 saves, but Price was left largely alone to protect a 1-0 lead, though he didn't see it that way.

"When a team's down a goal, that usually means a lot of pucks are going to be shot towards the net," Price said. "My guys did an excellent job of boxing them out and not letting them get to any rebounds."

Biron finished with 27 saves, needing only five in the third period, to drop his career record against Montreal to 14-11-2.

The Canadiens continued their tremendous run since a 4-1 loss in Tampa on Dec. 30, improving to 10-2-3 since then.

The Rangers, meanwhile, extended their winless streak to four games (0-3-1) and have only three wins in their last 10 games (3-6-1).

Rangers coach John Tortorella said he's liked how his team has played through this difficult stretch, but ultimately it matters little if the number in the win column doesn't change.

"For the past four games, we can talk about doing this well or that well, but we haven't won," he said. "We have to find a way to make a key play at a key time to change the momentum or to score a goal to win a hockey game."

After scoring a power-play goal for three straight games, the Rangers squandered a glorious opportunity when they generated absolutely nothing offensively over four consecutive opportunities in the second period.

The Canadiens actually outshot the Rangers 3-1 over those four power plays, and Gomez scored the winner just 38 seconds after the final Canadiens penalty expired.

"We struggled to make two passes," Tortorella said. "It was a struggle just to make a pass. When there was a play available, we struggled to put two together. That's been a struggle for us for the past month or so, and at this time of year when you play such close games, that needs to kick in for you."

The game began with surprising intensity for a matinee, with both teams physically engaged, culminating in a fight between Rangers super-pest Sean Avery and seldom-used Canadiens defenseman Alexandre Picard, playing in place of the flu-ridden James Wisniewski.

"First of all, it's Sean Avery," Picard said, explaining his decision to get into his second career fight, both against the Rangers. "Second of all, I was on the ice and he already had his gloves off pushing my helmet in my face. I'm not known for that, but I got away without a scratch, so I guess that's a good thing."

The Canadiens came out for the second period seemingly intent on continuing that physical intensity, except it led to a steady stream of penalties, four in a row to Andrei Kostitsyn, P.K. Subban, Picard and Subban again.

Once New York failed to generate a single shot on the fourth power play, there was a sense the Canadiens would make them pay for failing to take advantage of the situation.

Sure enough, it happened at 18:34 of the second when Picard's shot from the point missed the net to the right of Biron and bounced off the lively Bell Centre end boards right to Gomez on the other side. The former Ranger calmly corralled the puck, went backhand to forehand and roofed home his seventh of the season, putting an end to a 10-game goalless drought.

"It's a good thing (Picard) can't hit the net," Gomez said. "I'm sure he'll say he meant to do that. I just closed my eyes and got a little lucky."

That "luck" combined with a hot goalie to get the Canadiens a big two points, a formula they will attempt to reproduce in another matinee Sunday against the recently improved New Jersey Devils.